What legitimizes political theories?
That it "works" (there can be many definitions for this)?
That some people (e.g. authorities) agree on it?
That a majority agrees on it?
I personally think that one needs to rely at least on "what works", because humans must be able to coexist in some some structured manner. I.e. having humans attacking each other constantly wouldn't be beneficial for the group. Thus the physical and biological circumstances decide what rules will be applied. Thus political legitimizing could come from experimenting in "the nature". However, I speculate that this is not how all political beliefs behave, because some of them contain very abstract ideas about the state of things, not necessarily empirical, nor do they necessarily apply on very large groups. This poses some problems for "state-wide" political philosophies, because how could they know what everyone wants? Still there are some things that are rational in a very wide, even global manner. Such as the prohibition from causing physical harm or killing.